Integrated circuits are being fabricated with increasingly smaller components and interconnects. Metal interconnects, including etched aluminum interconnects and copper damascene interconnects, have difficulty handling increasing current densities. Moreover, it is sometimes desirable to reduce the thickness of the interconnects, exacerbating the current density problem. Graphene, having a very high in-plane electrical conductivity, has been proposed as an interconnect material. However, graphene layers more than a few atomic layers thick tend to exhibit degraded conductivity. Integrating thin layers of graphene into integrated circuits has been problematic, due to distortion of the graphene by dielectric materials contacting the graphene.